Additional knowledge for determining and interpreting feasible band boundaries in self-modeling/multivariate curve resolution of two-component systems

Recently Tauler's mcrbands Matlab script and Maeder's grid method were used by Abdollahi et al. to calculate the elements of transformation matrix for obtaining feasible band boundaries in multivariate curve resolution of a two-component system. Neither method is analytical, instead they are iterative. For long time it is well-known that Lawton and Sylvestre's approach can provide the feasible band boundaries analytically and non-iteratively. In this paper, firstly in the literature, the clear relationship is given between Lawton and Sylvestre's approach and Tauler's approach (as well as Maeder's approach). It was found that all approaches are identical for noiseless or moderately noisy two-component systems and, it was illustrated by figures and tables provided in Supplementary Material.